Sloppy assesment now becomes my problem!

On the 4th of September 2019 we were involved in an accident where a woman failed to stop behind us, where we already stopped at a red light, and bumped into the rear of our car. We took the car for an assessment where, to my confusion, the assessor noted the damage to the bumper but not the tow bar which BEING IN FRONT OF THE bumper took the brunt of the collision. They then denied my claim as it was less than the excess and told me claim myself from the other parties insurer. I then went to get my own quotes for the bumper and the tow bar and submitted it to the other parties' insurer. After 2 months of waiting the insurer of the other party ignored mu quotes and only took into consideration Outsurance ridiculous assessment for the bumper. This is their reply

"Thank you for the email received, please be advised as you are claiming from the other party directly Outsurance cannot intervene. With regards to the assessmnt, we base the assessment as per our rates (which are lower) and on a naked eye, which means additionals damages are attended when the car is in at the reapirers when claiming through Outsurance. I would advise you get a quote from any service provider so that the other party insurer can assist accordingly, our quote is always lower cause it's based on our rates and we get a discount.

I had no choice to do this myself, because my claim was rejected, so when would the extra repairs be noted? And I did get quotes myself which was rejected by the other party because it was not noted on the assessment!

What a mess! Now I can't fix my car. Thanks a lot!